Gay marriage supporters cheer during a rally moments before hearing that Proposition 8 had been overturned outside the Ninth Circuit Courthouse in San Francisco, Calif., on Feb. 7, 2012. A federal court later declined an appeal to revisit California's gay marriage ban in June, clearing the way for the Supreme Court to consider whether the ban violates the U.S. Constitution.

Gay rights groups cheered the Obama administration’s weighing in on a landmark Supreme Court case to allow same-sex marriage, while opponents decried the move as “war.”

But ultimately, constitutional and Supreme Court scholars say the government’s action of filing a legal brief on Thursday in support of repealing California’s Proposition 8, which bans gay marriage, will have little impact on the outcome of the case though it would carry some symbolic meaning.

Previous administrations have weighed in on cases brought to the nation’s highest court in which they were not directly involved -- such as the Truman and Eisenhower presidencies over the desegregation of schools, and the Reagan administration urging the justices to overrule the legalization of abortion, said Michael Klarman, a Harvard Law School professor and author of “From the Closet to the Altar: Courts, Backlash, and the Struggle for Same-Sex Marriage.”

“I don’t think that the government’s brief (on Prop. 8) would be that influential and I don’t say that because I think in general that’s the case, but I think everybody already knew what the administration’s position was,” he told NBC News.

“The president has made this such a salient issue and has been so clear about his position that I don’t think the brief really adds anything that we didn’t know,” he added, referring to Obama’s calls since last May for same-sex couples to have the right to marry, including his reference to the issue in his 2013 inaugural address.

The justices will hear oral arguments on Prop. 8 on March 26, with a decision expected in June.

In the legal filing, the Justice Department went further than the California case and suggested it was unconstitutional to block gay couples from getting married in at least seven other states where civil unions are offered instead. Those states, the department said, violate the Constitution if they offer civil unions to gay couples but deny them the right to marry.

While the administration takes no position in its brief beyond those states, its reasoning would have even broader implications. If the administration's legal theory were ultimately accepted, no state could, under constitutional guarantees against discrimination, deny same sex couples the right to marry.

But the administration is technically not a litigant to the Prop. 8 case, like it is in the other case that the justices will hear in late March over the constitutionality of the Defense of Marriage Act, a federal law barring recognition of same-sex couples.

G. Edward White, author of "The American Judicial Tradition: Profiles of Leading American Judges” and a Supreme Court scholar at the University of Virginia School of Law, said he thought the legal impact of the administration’s move in Prop. 8 would be “virtually zero.”

“I really don’t think one should attach any legal significance to this particular intervention,” he said before the brief was released.

Noting that Obama “been quite late to alter his view on same-sex marriage” -- he did so last May, announcing he supported it -- White thought this was a way to remind everybody that the administration “has now officially changed its mind on the issue.”

“My takeaway is really that this is a symbolic act on the part of the administration,” he said. “They’re doing it for political currency purposes. The justices are going to understand that’s what it is.”

William Eskridge, a professor at Yale Law School and a constitutional law expert who has authored many works on legal issues facing same-sex couples, said he didn’t think the brief would “necessarily change any minds” or be “as important for the outcome of the case” as the separate filings this week by about 130 notable Republicans as well as large businesses in support of same-sex marriage.

Klarman, of Harvard, agreed, saying he thought the brief by the Republicans could influence Justice Anthony Kennedy, whom he considers the swing vote on gay marriage.

“I think someone like Justice Kennedy … is interested among other things in how much political backlash there would be to a ruling in favor of gay marriage. The fact that there's so many Republicans now committing to support it is highly relevant,” he said.

“I think it matters that Obama was re-elected," he also noted. "If there were a President Romney who would be committed to opposing the decision then I think, you know, a swing justice might be more hesitant. I think it matters that Obama is president and I think it matters that Obama already came out in favor of this, but I don’t think the brief really adds much information.”

Though the experts don’t expect the legal briefs to carry much weight among the justices, parties on both sides of the issue were roused by the move.

ProtectMarriage.com, which brought the legal challenge to keep Prop. 8 on the books after the state of California decided not to defend it, decried the effort, calling it a “frontal assault” on the law by the Solicitor General in an email to supporters.

The group also said the bid was “a stunning declaration of war against the longstanding meaning of marriage and its obvious ties to society’s interesting in both mothers and fathers raising the next generation.”

Meanwhile, the American Foundation for Equal Rights, the sole sponsor of the challenge to Prop. 8 that also organized the brief by moderate and conservative Republicans as well as Libertarians, welcomed the government to its side.

“The brief filed by the Solicitor General is a powerful statement that Proposition 8 cannot be squared with the principles of equality upon which this nation was founded,” the group said in a statement. “AFER looks forward to having Solicitor General (Donald) Verrilli and the federal government by our side as we make the case for marriage equality for all before the Supreme Court.”